{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Hierarchical Partial Pooling"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose you are tasked with estimating baseball batting skills for several players. One such performance metric is batting average. Since players play a different number of games and bat in different positions in the order, each player has a different number of at-bats. However, you want to estimate the skill of all players, including those with a relatively small number of batting opportunities.\n",
    "\n",
    "So, suppose a player came to bat only 4 times, and never hit the ball. Are they a bad player?\n",
    "\n",
    "As a disclaimer, the author of this notebook assumes little to non-existant knowledge about baseball and its rules. The number of times at bat in his entire life is around \"4\".\n",
    "\n",
    "\n",
    "## Data\n",
    "\n",
    "We will use the [baseball data for 18 players from Efron and Morris](http://www.swarthmore.edu/NatSci/peverso1/Sports%20Data/JamesSteinData/Efron-Morris%20Baseball/EfronMorrisBB.txt) (1975).\n",
    "\n",
    "\n",
    "## Approach\n",
    "\n",
    "We will use PyMC3 to estimate the batting average for each player. Having estimated the averages across all players in the datasets, we can use this information to inform an estimate of an additional player, for which there is little data (*i.e.* 4 at-bats).\n",
    "\n",
    "In the absence of a Bayesian hierarchical model, there are two approaches for this problem:\n",
    "\n",
    "(1) independently compute batting average for each player (no pooling)\n",
    "(2) compute an overall average, under the assumption that everyone has the same underlying average (complete pooling)\n",
    "\n",
    "Of course, neither approach is realistic. Clearly, all players aren't equally skilled hitters, so the global average is implausible. At the same time, professional baseball players are similar in many ways, so their averages aren't entirely independent either. \n",
    "\n",
    "It may be possible to cluster groups of \"similar\" players, and estimate group averages, but using a hierarchical modeling approach is a natural way of sharing information that does not involve identifying *ad hoc* clusters.\n",
    "\n",
    "The idea of hierarchical partial pooling is to model the global performance, and use that estimate to parameterize a population of players that accounts for differences among the players' performances. This tradeoff between global and individual performance will be automatically tuned by the model. Also, uncertainty due to different number of at bats for each player (*i.e.* informatino) will be automatically accounted for, by shrinking those estimates closer to the global mean.\n",
    "\n",
    "For far more in-depth discussion please refer to Stan [tutorial](http://mc-stan.org/documentation/case-studies/pool-binary-trials.html) on the subject. The model and parameter values were taken from that example.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import pymc3 as pm\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import theano.tensor as tt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can load the dataset using pandas:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = pd.read_csv(pm.get_data('efron-morris-75-data.tsv'), sep=\"\\t\")\n",
    "at_bats, hits = data[['At-Bats', 'Hits']].values.T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's develop a generative model for these data.\n",
    "\n",
    "We will assume that there exists a hidden factor (`phi`) related to the expected performance for all players (not limited to our 18). Since the population mean is an unknown value between 0 and 1, it must be bounded from below and above. Also, we assume that nothing is known about global average. Hence, a natural choice for a prior distribution is the uniform distribution.\n",
    "\n",
    "Next, we introduce a hyperparameter `kappa` to account for the variance in the population batting averages, for which we will use a bounded Pareto distribution. This will ensure that the estimated value falls within reasonable bounds. These hyperparameters will be, in turn, used to parameterize a beta distribution, which is ideal for modeling quantities on the unit interval. The beta distribution is typically parameterized via a scale and shape parameter, it may also be parametrized in terms of its mean $\\mu \\in [0,1]$ and sample size (a proxy for variance) $\\nu = \\alpha + \\beta (\\nu > 0)$.\n",
    "\n",
    "The final step is to specify a sampling distribution for the data (hit or miss) for every player, using a Binomial distribution. This is where the data are brought to bear on the model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We could use `pm.Pareto('kappa', m=1.5)`, to define our prior on `kappa`, but the Pareto\n",
    "distribution has very long tails. Exploring these properly\n",
    "is difficult for the sampler, so we use an equivalent\n",
    "but faster parametrization using the exponential distribution.\n",
    "We use the fact that the log of a Pareto distributed\n",
    "random variable follows an exponential distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = len(hits)\n",
    "\n",
    "with pm.Model() as baseball_model:\n",
    "    \n",
    "    phi = pm.Uniform('phi', lower=0.0, upper=1.0)\n",
    "    \n",
    "    kappa_log = pm.Exponential('kappa_log', lam=1.5)\n",
    "    kappa = pm.Deterministic('kappa', tt.exp(kappa_log))\n",
    "\n",
    "    thetas = pm.Beta('thetas', alpha=phi*kappa, beta=(1.0-phi)*kappa, shape=N)\n",
    "    y = pm.Binomial('y', n=at_bats, p=thetas, observed=hits)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Recall our original question was with regard to the true batting average for a player with only 4 at bats and no hits. We can add this as an additional variable in the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "with baseball_model:\n",
    "    \n",
    "    theta_new = pm.Beta('theta_new', alpha=phi*kappa, beta=(1.0-phi)*kappa)\n",
    "    y_new = pm.Binomial('y_new', n=4, p=theta_new, observed=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now fit the model using MCMC:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [theta_new, thetas, kappa_log, phi]\n",
      "Sampling 2 chains: 100%|██████████| 6000/6000 [00:14<00:00, 425.56draws/s]\n",
      "The number of effective samples is smaller than 10% for some parameters.\n"
     ]
    }
   ],
   "source": [
    "with baseball_model:\n",
    "    trace = pm.sample(2000, tune=1000, chains=2,\n",
    "                      target_accept=0.95)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can plot the posteriors distribution of the parameters. First, the population hyperparameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.traceplot(trace, var_names=['phi', 'kappa']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hence, the population mean batting average is in the 0.22-0.31 range, with an expected value of around 0.26.\n",
    "\n",
    "Next, the estimates for all 18 players in the dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x547.2 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "player_names = data.apply(lambda x: x.FirstName + ' ' + x.LastName, axis=1)\n",
    "_, ax = pm.forestplot(trace, var_names=['thetas'])\n",
    "ax[0].set_yticklabels(player_names.tolist());"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, let's get the estimate for our 0-for-4 player:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x144 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.traceplot(trace, var_names=['theta_new']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that, despite the fact our additional player did not get any hits, the estimate of his average is not zero -- zero is not even a highly-probably value. This is because we are assuming that the player is drawn from a *population* of players with a distribution specified by our estimated hyperparemeters. However, the estimated mean for this player is toward the low end of the means for the players in our dataset, indicating that the 4 at-bats contributed some information toward the estimate."
   ]
  }
 ],
 "metadata": {
  "_draft": {
   "nbviewer_url": "https://gist.github.com/08078792809cc29b522253957464d5b7"
  },
  "anaconda-cloud": {},
  "gist": {
   "data": {
    "description": "hierarchical_partial_pooling.ipynb",
    "public": true
   },
   "id": "08078792809cc29b522253957464d5b7"
  },
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.5"
  },
  "latex_envs": {
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 0
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
